Differential forms on universal K3 surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912133245042688 |
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| author | Ma, Shouhei |
| author_facet | Ma, Shouhei |
| contents | We give a vanishing and classification result for holomorphic differential forms on smooth projective models of the moduli spaces of pointed K3 surfaces. We prove that there is no nonzero holomorphic k-form for 0<k<10 and for even k>19. In the remaining cases, we give an isomorphism between the space of holomorphic k-forms with that of vector-valued modular forms (9<k<19) or scalar-valued cusp forms (odd k>18) for the modular group. These results are in fact proved in the generality of lattice-polarization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02550 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Differential forms on universal K3 surfaces Ma, Shouhei Algebraic Geometry 14J28, 14J15, 11F55 We give a vanishing and classification result for holomorphic differential forms on smooth projective models of the moduli spaces of pointed K3 surfaces. We prove that there is no nonzero holomorphic k-form for 0<k<10 and for even k>19. In the remaining cases, we give an isomorphism between the space of holomorphic k-forms with that of vector-valued modular forms (9<k<19) or scalar-valued cusp forms (odd k>18) for the modular group. These results are in fact proved in the generality of lattice-polarization. |
| title | Differential forms on universal K3 surfaces |
| topic | Algebraic Geometry 14J28, 14J15, 11F55 |
| url | https://arxiv.org/abs/2301.02550 |